Ph.D.'s in Number Theory at the University of Michigan

The following is a list of the Ph.D. degrees awarded in number theory, including the dissertation title, the thesis advisor, and (when known) the first post-Ph.D. place of employment.


Corey Everlove
(Lagarias) University of Michigan

Brandon Carter
Jochnowitz congruences at residual primes
(Prasanna) Google

Charlotte Chan
Period identities of CM forms on quaternion algebras
(Prasanna) Princeton University


Daniel Barter
Some remarks about the interaction between quantum algebra and representation stability
(Snowden) Australian National University

Gene Kopp
Indefinite theta functions and zeta functions
(Lagarias) University of Bristol


Adam Kaye
Arithmetic of the Asai L-function for Hilbert modular forms
(Prasanna) Goldman Sachs

Suchandan Pal
An explicit Jacquet–Langlands correspondence
(Prasanna) Mavenir


Ariel Shnidman
Heights of generalized Heegner cycles
(Prasanna) Boston College


Harry Altman
Integer complexity, addition chains, and well-ordering

Sijun Liu
Functional equations involving Laurent polynomials and meromorphic functions, with applications to dynamics and Diophantine equations
(Zieve) Oracle

Hieu Ngo
Generalizations of the Lerch zeta functions
(Lagarias) Texas A&M University at Qatar


Hunter Brooks
Generalized Heegner cycles, Shimura curves, and special values of p-adic L-functions
(Prasanna) EPFL - Switzerland

Alex Mueller
Applications of generalized Fermat varieties to zeta functions of Artin-Schreier curves
(Zieve) Less Annoying CRM

Julian Rosen
The arithmetic of multiple harmonic sums
(Lagarias) Waterloo

Zach Scherr
Rational polynomial Pell equations
(Zieve) Penn


Ben Weiss
Diophantine equations with two separated variables
(Lagarias/Zieve) Technion


Johnson Jia
The arithmetic of the Yoshida lift
(Skinner/DeBacker) University of British Columbia

Brian Wyman
Polynomial decomposition over rings


Jonathan Bober
Integer ratios of factorials, hypergeometric series, and related step functions
(Lagarias) Institute for Advanced Study

Ellen Eischen
p-adic differential operators on automorphic forms and applications
(Skinner/Ramsey) Northwestern University

Leo Goldmakher
Multiplicative mimicry and improvements of the Polya-Vinogradov theorem
(Soundararajan/Lagarias) University of Toronto

Hester Graves
On Euclidean ideal classes
(Ramsey) Queen's University

Wansu Kim
Galois deformation theory for norm fields and its arithmetic applications
(Conrad/DeBacker) Imperial College


Craig Spencer
Analytic methods for Diophantine problems
(Wooley/Lewis) Institute for Advanced Study


Mahesh Agarwal
p-Adic L-functions for GSp(4) x GL(2)
(Skinner) McMaster University

Bryden Cais
Compatabilities, correspondences, and integral structure in p-adic cohomology
(Conrad) McGill University

Rizwanur Khan
Non-vanishing of the symmetric square L-function
(Soundararajan) UCLA

Matthew Smith
On solution-free sets for simultaneous additive equations
(Wooley) University of Georgia


Trevor Arnold
Anticyclotomic Iwasawa Theory for Modular Forms
(Skinner) University of Washington

Krzysztof Klosin
Congruences among automorphic forms on the unitary group U(2,2)
(Skinner) University of Utah


Peng Gao
n-level densities of zeros of quadratic Dirichlet L-functions
(Montgomery/Soundararajan) AIM/Montreal

Sreekar Shastry
J_1(n) has connected fibers
(Conrad) Tata Institute (Bombay)


Tobias Berger
Eisenstein ideal for imaginary quadratic fields
(Skinner) Cambridge University

Jim Brown
Sato-Kurokawa lifts and L-values
(Skinner) Ohio State University

Tong Liu
Potentially good reduction of Barsotti-Tate groups
(Conrad) University of Pennsylvania


Mihran Papikian
Optimal elliptic curves and degree conjecture over function fields
(Conrad) Stanford University


Tsz Ho Chan
Pair correlation and distribution of prime numbers
(Montgomery) Case Western Reserve University


Michael Knapp
Forms in many variables over p-adic fields
(Wooley) University of Rochester

Joseph Palen
Bounds for class members of cyclotomic function fields


Eric Freeman
Quadratic and cubic diophantine inequalities

Scott Parsell
Exponential sums and diophantine problems

Victor Scharaschkin
Local-global problems and the Brauer-Manin obstruction


Matt DeLong
Relating elliptic curves to three-ranks of quadratic number fields

Pierre Giguere
On the conjecture of Langlands and Rapoport

Tony Vazzana
4-ranks of K_2 of rings of integers in quadratic number fields

Joel Wisdom
On the representations of numbers as sums of powers


Greg Martin
The distribution of prime primitive roots and dense Egyptian fractions


Stefan Treatman
Euclidean systems


Morley Davidson
Waring's problem in number fields


Mary Armon
Sums of quadratic characters


Matthias Pfau
The reduction of connected Shimura varieties at primes of good reduction

David Santos
Sets of monotonicity for the Riemann zeta-functions

Wafa Wei
Weil numbers and generating large field extensions


Kent Boklan
The asymptotic formula in Waring's problem

Hemar Godinho
A pair of additive quartic forms


John Rickert
Simultaneous rational approximations and related Diophantine equations


Daniel Kornhauser
Bounds for the smallest integer solution of general quadratic equations

Jungseob Lee
On the constant in the Turan-Kubilius inequality

Thomas Martin
Minimal theta functions

Noel Wass
Algebraic independance of the values at algebraic points of a class of functions considered by Mahler


David Folk
On the genus of normal closures of rational function field extensions

Fred Schultheis
Explicit reciprocity laws in algebraic function fields


Capi Corrales-Rodriganez
Nevanlinna theory in the p-adic plane


Jerome Solinas
A theorem of metric Diophantine approximation and estimates for sums involving binary digits


Todd Cochrane
Small solutions of congruences


Russell Lyons
A characterization of measures whose Fourier-Stiltjes transforms vanish at infinity


William Hawkins, Jr.
The etale cohomology of certain p-torsion sheaves

Ali Özlük
Pair correlation of zeros of Dirichlet L-functions


Brian Conrey
Zeros of derivatives of Riemann's XI function on the critical line

David Leep
Common value properties of quadratic forms

William Monach
Numerical investigation of several problems in number theory

Michael Robinson
Topics in the theory of irrational numbers


Steve Gonek
Analytic properties of zeta and L-functions

William Miller
Transcendence measures for values of analytic solutions to certain functional equations

Patrick Morton
The 2-classgroup of a quadratic number field and the Pell equation X^2- delta Y^2 = -1


Andrew Baily
On the density of discriminants of quartic fields

Piotr Blass
Zariski surfaces

Sidney Graham
Applications of sieve methods

Gerry Myerson
Equations in finite fields


Michal Bester
Local flat duality of abelian varieties

John Driggs
Approximations to solutions over henselian rings

Stephen Ricci
Local distribution of primes


Ralph Toliver
Bounds for solutions of two simultaneous additive equations of odd degree


Fern Ellison
Three diagonal quadratic-forms

Henry Thomas, Jr.
A numerical approach to Waring's problem for fourth powers


Maurice Craig
Irregular discriminants


Erik Lippa
Hecke operators for modular forms of genus R

Catherine Stahl
Systems of additive equations over algebraic number fields


Robert Kubota
Waring's problem in FQ[X]

Susan Schuur
Systems of quadratic forms over local fields


Michael Fried
Value sets of polynomials

Charles Ryavec
Problems in diophantine analysis

Gretchen Wagner
Module decompositions of ideals in Dedekind domains


Charles MacCluer
On exceptional polynomials


Underwood Dudley
The distribution modulo 1 of oscillating functions

Joseph Heisler
Diophantine problems for matrix rings, rings of functions, and other rings


Elizabeth Grobe
Some `p'-adic and `g'-adic versions of Roth's theorem


Thomas Walker, Jr.
Two metric theorems in Diophantine approximation


Klaus Guting
About algebraic and transcendental numbers


Donald J. Lewis
Cubic homogeneous polynomials over a p-adic number field